Serif mask design for correcting severe corner rounding and line end shortening in lithography

Abstract

A photolithographic mask for conducting illumination from a light source onto a semiconductor surface during a microlithographic manufacturing process. The mask includes a line end portion of a width w and including two corners, each corner defining a respective region for locating one or more serifs for correcting severe corner rounding and line end foreshortening effects caused by the optical diffraction during the optical imaging process. For aerial image/resist pattern modeled as a convolution or the square of a convolution between the photomask and an intensity/amplitude kernel function having an effective range r in x and y directions, and under a condition that w<r<2w, a hanging square serif of a size w×w is provided attached to a respective corner within a corner region. For the condition of 2nw<r≦2(n+1)w, with n=1, 2, . . . , each corner region includes an associated (n+1) serifs, each being linearly aligned along line-end extension line and spaced apart from an adjacent serif by a distance w, with each of the first n serifs being square and of a width w, and the (n+1) th serif being a rectangle of a length w and a width min(r-2nw, w). When the intensity/amplitude kernel function is modeled as being azimuthal-angle independent and being non-zero over a circular area of radius r, which is typical for usual circular aperture, the serif size in the corner regions may be optimized. For a hanging square serif of size w×w under the condition w<r≦2w, if further w<r<√2 w, then the hanging serif in each corner region may be reduced in size without altering the aerial image/resist pattern intensity at its respective corner. The portion of the square serif to be removed is that portion of the square which is outside the circular intensity/amplitude kernel function of radius r centered at its respective corner. For a set of associated (n+1) serifs under a condition 2nw<r≦2(n+1)w, if further [(2n+1) 2 +1] 1/2 w≦r ≦2(n +1)w, with n=1, 2, . . . , then the (n+1) th serif in each corner region may be reduced in size without altering the aerial image/resist pattern intensity at its respective corner. The portion of the (n+1) th serif to be removed is that portion of the rectangle which is outside the circular intensity/amplitude kernel function of radius r centered at its respective corner.

What is claimed is: 
     
       1. A method for designing a photolithographic mask pattern including serifs for correcting severe corner rounding and line end foreshortening effects occurring in a line-end portion of a microlithographic circuit as a result of a photolithographic process, said method including: modeling aerial image intensity or final photoresist pattern for said photolithographic process as a convolution or the square of a convolution between said mask and an intensity/amplitude kernel function having an effective range r in x and y directions;   designing said mask to include a line end portion of a width w and including an edge defining two corners for illumination by an imaging system during said photolithographic process, each corner having an associated corner region outside said line-end portion for locating of one or more serifs, whereby for closely spaced lines in said mask, said serif functions as a co-serif of two or more nearby wire lines.   
     
     
       2. The method as claimed in claim 1, further including representing, for implementation of spatially incoherent illumination or partial coherent illumination with large coherence factor σ, an aerial image intensity or photoresist pattern of the lithographic process as a convolution between said mask and an intensity kernel function having an effective range r. 
     
     
       3. The method as claimed in claim 1, further including representing, for implementation of spatially coherent illumination or partial coherent illumination with small coherence factor σ, an aerial image intensity or photoresist pattern of the lithographic process as the square of a convolution between said mask and an amplitude kernel function having an effective range r. 
     
     
       4. The method as claimed in claim 1, further including modeling said effective range r as a function of the wavelength λ of the illumination light, a numerical aperture "NA" of the imaging system, and a coherence factor σ, and one of: modeling said effective range r on the order of λ/NA, or modeling said effective range r based on a range of optical proximity effects. 
     
     
       5. The method as claimed in claim 1, further including modeling an intensity/amplitude kernel function K(x, y) as having symmetry according to: K(x, y)=K(|x|, |y|)=K(y, x), where x=y=0 represents a center of said kernel function. 
     
     
       6. The method as claimed in claim 1, wherein each respective corner region is an area defined between lines extending from each corner of said end line portion. 
     
     
       7. The method as claimed in claim 1, wherein for a condition that w<r<2w, providing a hanging square serif of a size w×w within a corner region attached to a respective corner at a single point. 
     
     
       8. The method as claimed in claim 1, wherein for a condition of 2nw<r≦2(n+1)w, with n=1, 2, . . . , designing each said corner region of said line end portion to include an associated (n+1) serifs, each of the first n serifs being square and of a width w, and the (n+1) th  serif being a rectangle of a length w and width min(r-2nw, w). 
     
     
       9. The method as claimed in claim 8, wherein within each corner region, each of said (n+1) associated serifs are linearly aligned along line-end extension line and spaced apart from an adjacent serif by a distance w, a first said serif being a hanging serif connected to said corner at one point only. 
     
     
       10. The method as claimed in claim 1, further including the step of modeling the intensity/amplitude kernel function as being azimuthal-angle independent and being non-zero over a circular area of radius r when implementing a circular aperture, said method further including the step of further optimizing the serif design without affecting the aerial image intensity at the corner. 
     
     
       11. The method as claimed in claim 10, wherein for a condition of max (2nw, w)<r<[(2n+1) 2  +1] 1/2  w, with n=0, 1, 2, . . . , drawing a circular area of radius r with its center at the respective corner, which represents said intensity/amplitude kernel function, said circle intersecting the (n+1)th serif in respective corner region. 
     
     
       12. The method as claimed in claim 11, wherein said (n+1) th  serif intersected by a intensity/amplitude kernel function circular area of radius r which centers at a corner defines a portion to be removed from said serif. 
     
     
       13. The method as claimed in claim 12, wherein for an instance when [(2n+1) 2  +1] 1/2   w≦r≦2(n+1)w, the (n+1)th serif is not intersected by said intensity/amplitude kernel function circular area. 
     
     
       14. The method as claimed in claim 1, including the step of locating said serifs between two or more neighboring wire tracks in a minimum-pitch wire/space array of a photolithographic circuit, wherein each wire track is occupied, said serifs providing optical proximity correction for those neighboring wires and comprise co-serifs of said two or more neighboring wires. 
     
     
       15. The method as claimed in claim 14, including the step of locating said serifs between two or more neighboring tracks in a minimum-pitch wire/space array of a photolithographic circuit, wherein alternating wire tracks are occupied, said serifs providing optical proximity correction for those neighboring wires and comprise co-serifs of said two or more neighboring wires. 
     
     
       16. A photolithographic mask for conducting a light source onto a semiconductor surface during a photolithographic process, said mask including a line end portion for illumination by an imaging system, wherein an aerial image intensity or final photoresist pattern for said photolithographic process is modeled as a convolution or the square of a convolution between said mask and an intensity/amplitude kernel function having an effective range r in x and y directions, said line end portion having a width w and including two corners each defining a respective corner region being an area defined between lines extending from each corner of said end line portion for locating one or more serifs therein for correcting severe corner rounding and line end foreshortening effects caused by said mask during said photolithographic process, whereby for closely spaced lines, a serif functions as a co-serif of two or more nearby wire lines. 
     
     
       17. The photolithographic mask as claimed in claim 16, wherein for a condition that w<r<2w, providing a hanging square serif of a size w×w attached to a respective corner within a corner region at a single point only. 
     
     
       18. The photolithographic mask as claimed in claim 16, wherein for a condition of 2nw<r≦2(n+1)w, with n=1, 2, . . . , each said corner region of said line end portion includes an associated (n+1) serifs, each of the first n serifs being square and of a width w, and the (n+1) th  serif being a rectangle of a length w and width min(r-2nw, w). 
     
     
       19. The photolithographic mask as claimed in claim 18, wherein within each corner region, each of said (n+1) associated serifs are linearly aligned along a line-end extension line and spaced apart from an adjacent serif by a distance w, said first serif being a hanging serif connected to said corner at one point. 
     
     
       20. The photolithographic mask as claimed in claim 16, wherein said imaging system includes a light source device having a square or circular aperture. 
     
     
       21. The photolithographic mask as claimed in claim 17, wherein for an imaging system including a light source device including a circular aperture wherein the intensity/amplitude kernel function is modeled as being azimuthal-angle independent and being non-zero over a circular area of radius r, a hanging square serif of size w×w is optimized without affecting the aerial image intensity at the corner. 
     
     
       22. The photolithographic mask as claimed in claim 18, wherein for an imaging system including a light source device including a circular aperture wherein the intensity/amplitude kernel function is modeled as being azimuthal-angle independent and being non-zero over a circular area of radius r, a hanging square serif of size w×w and the associated (n+1) serifs are optimized without affecting the aerial image intensity at the corner. 
     
     
       23. The photolithographic mask as claimed in claim 22, wherein for a condition of max (2nw, w)<r<[(2n+1) 2  +1] 1/2  w, with n=0, 1, 2, . . . , each said corner region includes an associated (n+1) serifs, each of the first n serifs being square and of a size w×w, and the (n+1) serif in each corner region being intersected by said intensity/amplitude kernel function of circular area of radius r when centered at its respective corner. 
     
     
       24. The photolithographic mask as claimed in claim 23, wherein said (n+1) th  serif intersected by a intensity/amplitude kernel function circular area of radius r which centers at a corner defines a portion to be removed from said serif. 
     
     
       25. The photolithographic mask as claimed in claim 24, wherein for an instance when [(2n+1) 2  +1] 1/2   w≦r≦2(n+1)w, the (n+1) th  serif is not intersected by said intensity/amplitude kernel function circular area. 
     
     
       26. The photolithographic mask as claimed in claim 16, applied between two or more neighboring tracks in a minimum-pitch wire/space array of a photolithographic circuit, wherein each wire track is occupied, said serif mask providing optical proximity correction for those neighboring wires and comprise co-serifs of said two or more neighboring wires. 
     
     
       27. The photolithographic mask as claimed in claim 16, applied between two or more neighboring tracks in a minimum-pitch wire/space array of a photolithographic circuit, wherein alternating tracks are occupied, said serif mask providing optical proximity correction for those neighboring wires and comprising co-serifs of said two or more neighboring wires.